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Why Are There 5,280 Feet in a Mile?

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Why are there 5,280 feet in a mile, and why are nautical miles different from the statute miles we use on land? Why do we buy milk and gasoline by the gallon? Where does the abbreviation "lb" come from? Let's take a look at the origins of a few units of measure we use every day.

The Mile

The basic concept of the mile originated in Roman times. The Romans used a unit of distance called the mille passum, which literally translated into "a thousand paces." Since each pace was considered to be five Roman feet—which were a bit shorter than our modern feet—the mile ended up being 5,000 Roman feet, or roughly 4,850 of our modern feet.

If the mile originated with 5,000 Roman feet, how did we end up with a mile that is 5,280 feet? Blame the furlong. The furlong wasn't always just an arcane unit of measure that horseracing fans gabbed about; it once had significance as the length of the furrow a team of oxen could plow in a day. In 1592, Parliament set about determining the length of the mile and decided that each one should be made up of eight furlongs. Since a furlong was 660 feet, we ended up with a 5,280-foot mile.

The Nautical Mile

So if the statute mile is the result of Roman influences and plowing oxen, where did the nautical mile get its start? Strap on your high school geometry helmet for this one.

Each nautical mile originally referred to one minute of arc along a meridian around the Earth. Think of a meridian around the Earth as being made up of 360 degrees, and each of those degrees consists of 60 minutes of arc. Each of these minutes of arc is then 1/21,600th of the distance around the earth. Thus, a nautical mile is 6,076 feet.

The Acre

Like the mile, the acre owes its existence to the concept of the furlong. Remember that a furlong was considered to be the length of a furrow a team of oxen could plow in one day without resting. An acre—which gets its name from an Old English word meaning "open field"—was originally the amount of land that a single farmer with a single ox could plow in one day. Over time, the old Saxon inhabitants of England established that this area was equivalent to a long, thin strip of land one furlong in length and one chain—an old unit of length equivalent to 66 feet—wide. That's how we ended up with an acre that's equivalent to 43,560 square feet.

The Foot

As the name implies, scholars think that the foot was actually based on the length of the human foot. The Romans had a unit of measure called a pes that was made up of twelve smaller units called unciae. The Roman pes was a smidge shorter than our foot—it came in at around 11.6 inches—and similar Old English units based on the length of people's feet were also a bit shorter than our 12-inch foot. The 12-inch foot didn't become a common unit of measurement until the reign of Henry I of England during the early 12th century, which has led some scholars to believe it was standardized to correspond to the 12-inch foot of the king.

The Gallon

The gallon we use for our liquids comes from the Roman word galeta, which meant "a pailful." There have been a number of very different gallon units over the years, but the gallon we use in the United States is probably based on what was once known as the "wine gallon" or Queen Anne's gallon, which was named for the reigning monarch when it was standardized in 1707. The wine gallon corresponded to a vessel that was designed to hold exactly eight troy pounds of wine.

The Pound

Like several other units, the pound has Roman roots. It's descended from a roman unit called the libra. That explains the "lb" abbreviation for the pound, and the word "pound" itself comes from the Latin pondo, for "weight." The avoirdupois pounds we use today have been around since the early 14th century, when English merchants invented the measurement in order to sell goods by weight rather than volume. They based their new unit of measure as being equivalent to 7000 grains, an existing unit, and then divided each 7000-grain avoirdupois pound into 16 ounces.

The Horsepower

Early 18th-century steam engine entrepreneurs needed a way to express how powerful their machines were, and the industrious James Watt hit on a funny idea for comparing engines to horses. Watt studied horses and found that the average harnessed equine worker could lift 550 pounds at a clip of roughly one foot per second, which equated to 33,000 foot-pounds of work per minute.

Not all scholars believe that Watt arrived at his measurement so scientifically, though. One common story claims that Watt actually did his early tests with ponies, not horses. He found that ponies could do 22,000 foot-pounds of work per minute and figured that horses were half again stronger than ponies, so he got the ballpark figure of 33,000 foot-pounds of work per minute.

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iStock // Ekaterina Minaeva
Man Buys Two Metric Tons of LEGO Bricks; Sorts Them Via Machine Learning
May 21, 2017
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iStock // Ekaterina Minaeva

Jacques Mattheij made a small, but awesome, mistake. He went on eBay one evening and bid on a bunch of bulk LEGO brick auctions, then went to sleep. Upon waking, he discovered that he was the high bidder on many, and was now the proud owner of two tons of LEGO bricks. (This is about 4400 pounds.) He wrote, "[L]esson 1: if you win almost all bids you are bidding too high."

Mattheij had noticed that bulk, unsorted bricks sell for something like €10/kilogram, whereas sets are roughly €40/kg and rare parts go for up to €100/kg. Much of the value of the bricks is in their sorting. If he could reduce the entropy of these bins of unsorted bricks, he could make a tidy profit. While many people do this work by hand, the problem is enormous—just the kind of challenge for a computer. Mattheij writes:

There are 38000+ shapes and there are 100+ possible shades of color (you can roughly tell how old someone is by asking them what lego colors they remember from their youth).

In the following months, Mattheij built a proof-of-concept sorting system using, of course, LEGO. He broke the problem down into a series of sub-problems (including "feeding LEGO reliably from a hopper is surprisingly hard," one of those facts of nature that will stymie even the best system design). After tinkering with the prototype at length, he expanded the system to a surprisingly complex system of conveyer belts (powered by a home treadmill), various pieces of cabinetry, and "copious quantities of crazy glue."

Here's a video showing the current system running at low speed:

The key part of the system was running the bricks past a camera paired with a computer running a neural net-based image classifier. That allows the computer (when sufficiently trained on brick images) to recognize bricks and thus categorize them by color, shape, or other parameters. Remember that as bricks pass by, they can be in any orientation, can be dirty, can even be stuck to other pieces. So having a flexible software system is key to recognizing—in a fraction of a second—what a given brick is, in order to sort it out. When a match is found, a jet of compressed air pops the piece off the conveyer belt and into a waiting bin.

After much experimentation, Mattheij rewrote the software (several times in fact) to accomplish a variety of basic tasks. At its core, the system takes images from a webcam and feeds them to a neural network to do the classification. Of course, the neural net needs to be "trained" by showing it lots of images, and telling it what those images represent. Mattheij's breakthrough was allowing the machine to effectively train itself, with guidance: Running pieces through allows the system to take its own photos, make a guess, and build on that guess. As long as Mattheij corrects the incorrect guesses, he ends up with a decent (and self-reinforcing) corpus of training data. As the machine continues running, it can rack up more training, allowing it to recognize a broad variety of pieces on the fly.

Here's another video, focusing on how the pieces move on conveyer belts (running at slow speed so puny humans can follow). You can also see the air jets in action:

In an email interview, Mattheij told Mental Floss that the system currently sorts LEGO bricks into more than 50 categories. It can also be run in a color-sorting mode to bin the parts across 12 color groups. (Thus at present you'd likely do a two-pass sort on the bricks: once for shape, then a separate pass for color.) He continues to refine the system, with a focus on making its recognition abilities faster. At some point down the line, he plans to make the software portion open source. You're on your own as far as building conveyer belts, bins, and so forth.

Check out Mattheij's writeup in two parts for more information. It starts with an overview of the story, followed up with a deep dive on the software. He's also tweeting about the project (among other things). And if you look around a bit, you'll find bulk LEGO brick auctions online—it's definitely a thing!

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Opening Ceremony
These $425 Jeans Can Turn Into Jorts
May 19, 2017
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Opening Ceremony

Modular clothing used to consist of something simple, like a reversible jacket. Today, it’s a $425 pair of detachable jeans.

Apparel retailer Opening Ceremony recently debuted a pair of “2 in 1 Y/Project” trousers that look fairly peculiar. The legs are held to the crotch by a pair of loops, creating a disjointed C-3PO effect. Undo the loops and you can now remove the legs entirely, leaving a pair of jean shorts in their wake. The result goes from this:


Opening Ceremony

To this:


Opening Ceremony

The company also offers a slightly different cut with button tabs in black for $460. If these aren’t audacious enough for you, the Y/Project line includes jumpsuits with removable legs and garter-equipped jeans.

[h/t Mashable]